Results 11 to 20 of about 27,297,467 (168)
Type-Based Approaches to Rounding Error Analysis [PDF]
CoRRPhD thesis.
Kellison, Ariel Eileen
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Probabilistic Rounding Error Analysis of Householder QR Factorization [PDF]
SIAM Journal on Matrix Analysis and Applications, 2023 Abstract. The standard worst-case normwise backward error bound for Householder QR factorization of an [Formula: see text] matrix is proportional to [Formula: see text], where [Formula: see text] is the unit roundoff. We prove that the bound can be replaced by one proportional to [Formula: see text] that holds with high probability if
Michael P. Connolly, Nicholas J. Higham
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Numerical Fuzz: A Type System for Rounding Error Analysis [PDF]
Proceedings of the ACM on Programming LanguagesAlgorithms operating on real numbers are implemented as floating-point computations in practice, but floatingpoint operations introduce roundoff errors that can degrade the accuracy of the result. We propose Λ num
Ariel E. Kellison, Justin Hsu
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FPU-Supported Running Error Analysis [PDF]
Acta Polytechnica, 2010 A-posteriori forward rounding error analyses tend to give sharper error estimates than a-priori ones, as they use actual data quantities. One of such a-posteriori analysis – running error analysis – uses expressions consisting of two parts; one generates
T. Zahradnický, R. Lórencz
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Statistical Analysis of Rounded Data: Measurement Errors vs Rounding Errors [PDF]
Journal of Mathematical Sciences, 2018 Consider the measurements in which the discretization step is constant and without loss of generality is equal to 1. The measured value \(X\) is rounded to the closest integer \(X^*\) according to the rule \(X^*=[X+0.5]\) where \([x]\) is the integer part of \(x\). Measurements of the quantity \(\mu\) are considered as i.i.d. random samples \(X_1,\dots,
Ushakov, Nikolai, Ushakov, Vladimir G.
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A quantitative probabilistic investigation into the accumulation of rounding errors in numerical ODE solution. [PDF]
, 2009 We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs) from a probabilistic viewpoint. We show that the accumulation of rounding errors results in a solution which is inherently random and
Turner, Amanda, Mosbach, Sebastian
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Symmetric and Asymmetric Rounding [PDF]
, 2006 If rounded data are used in estimating moments and regression coefficients, the estimates are typically more or less biased. The purpose of the paper is to study the bias inducing effect of rounding, which is also seen when population moments instead of ...
Ahmad, A. S. +3 more
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Probabilistic Rounding and Sheppard's Correction [PDF]
, 2008 When rounded data are used in place of the true values to compute the variance of a variable or a regression line, the results will be distorted. Under suitable smoothness conditions on the distribution of the variable(s) involved, this bias, however ...
Komlos, John, Schneeweiß, Hans
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Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms [PDF]
SIAM Journal on Scientific Computing, 2021 Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speedups and lower storage cost if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from ...
Lucia Minah Yang +2 more
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Error Analysis of Band Matrix Method [PDF]
, 1984 Numerical error in the solution of the band matrix method based on the elimination method in single precision is investigated theoretically and experimentally, and the behaviour of the truncation error and the roundoff error is clarified.
Taniguchi, Takeo, Soga, Akira
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